3. The Electronic Journal Of Combinatorics A refereed allelectronic journal that welcomes papers in all branches of discrete mathematics, including all kinds of combinatorics, graph theory,http://www.combinatorics.org/

The Electronic Journal of Combinatorics

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Combinatorics

5. 05: Combinatorics combinatorics is, loosely, the science of counting. This is the area of mathematics in which we study families of sets (usually finite) with certainhttp://www.math.niu.edu/~rusin/known-math/index/05-XX.html

05: Combinatorics

Introduction

Combinatorics is, loosely, the science of counting. This is the area of mathematics in which we study families of sets (usually finite) with certain characteristic arrangements of their elements or subsets, and ask what combinations are possible, and how many there are. This includes numerous quite elementary topics, such as enumerating all possible permutations or combinations of a finite set. Consequently, it is difficult to mention in this page all the topics with which a person new to combinatorics might come into contact. Moreover, because of the approachable nature of the subject, combinatorics is often presented with other fields (elementary probability, elementary number theory, and so on) to the exclusion of the more significant aspects of the subject. These include more sophisticated methods of counting sets. For example, the cardinalities of sequences of sets are often arranged into power series to form the generating functions, which can then be analyzed using techniques of analysis. (Since many counting procedures involve the binomial coefficients, it is not surprising to see the hypergeometric functions appear frequently in this regard.) In some cases the enumeration is asymptotic (for example the estimates for the number of partitions of an integer). In many cases the counting can be done in a purely synthetic manner using the "umbral calculus". Combinatorial arguments determining coefficients can be used to deduce identities among functions, particularly between infinite sums or products, such as some of the famous Ramanujan identities.

Other links are provided too. From the review by A. T. White in I highly recommend this book to anyone with an interest in the topics, techniques, and/or algorithms of combinatorics.

Solutions to the exercises

The solutions are in PDF format: there is one file for each chapter. Only the first eleven chapters are available as yet (work in progress on the remainder), and detailed solutions to projects are not given.

From the book

8. The Combinatorics Net Annals of combinatorics will publish outstanding contributions to combinatorial mathematics in all its aspects. Special regard will be given to newhttp://www.combinatorics.net/

12. Algorithmic Combinatorics We are mainly interested in the connection of classical combinatorics, special functions, and computer algebra ( symbolic computation in combinatorics ).http://www.risc.uni-linz.ac.at/research/combinat/

13. Combinatorics & Optimization We are intensely research oriented and hold a strong international reputation in each of our six major areas Algebraic combinatorics,http://www.math.uwaterloo.ca/CandO_Dept/

15. Australasian Journal Of Combinatorics THE AUSTRALASIAN JOURNAL OF combinatorics. ISSN 10344942. Published for the Combinatorial Mathematics Society of Australasia (Inc.) by the Centre forhttp://ajc.maths.uq.edu.au/

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18. On-line Dictionary Of Combinatorics -- Moved The Online Dictionary of combinatorics has moved. The dictionary is now located at http//www.southernct.edu/~fields/comb_dic. Please update your links.http://www.math.uic.edu/~fields/comb_dic/

The On-line Dictionary of Combinatorics has moved

19. Enumerative Combinatorics Volume 1 of Enumerative combinatorics was published by Wadsworth Brooks/Cole in 1986. A second printing was published by Cambridge University Press inhttp://www-math.mit.edu/~rstan/ec/

Information on Enumerative Combinatorics

Volume 1 of Enumerative Combinatorics A paperback edition of Volume 1, second printing, is now available. It differs from the hardcover edition only in a slightly updated list of Errata and Addenda. Volume 2 was published around January 5, 1999. A paperback edition was published in June, 2001. Volumes 1 and 2 can be ordered online from Cambridge University Press ( volume 1 and volume 2 Amazon.com , or various other online book sellers.

Links to related material:

Volume 1

Table of contents for Volume 1. Short errors (three page PostScript file) for the first printing of Volume 1 corrected in the text of the second printing. Longer errors (eight page PostScript or PDF file) for the first printing of Volume 1, published in the second printing, hardcover edition of 1997, as Errata and Addenda on pages 319-325. Supplementary Problems (17 page PostScript file) without solutions for Volume 1. They do not appear in the first printing and are on pages 307-318 of the second printing. Additional corrections (nine page PostScript or PDF file; version of 28 February 2008) not found in time to include in the second printing.

20. University Of Michigan Combinatorics Seminar The University of Michigan combinatorics Seminar Winter 2008 Fridays 410500, 3866 East Hall. date, speaker, affiliation, title (click for an abstract)http://www.math.lsa.umich.edu/seminars/combin/